Until microsoft/TypeScript#5453 is implemented, you'll need to create multiple overloads, one for each number of arguments. For example, this is the type definition of a function which takes a function and returns a function with the same arguments but the result wrapped in a Promise.
declare function wrapPromise<R>(f: () => R): () => Promise<R>
declare function wrapPromise<A1, R>(f: (a1: A1) => R): (a1: A1) => Promise<R>
declare function wrapPromise<A1, A2, R>(f: (a1: A1, a2: A2) => R): (a1: A1, a2: A2) => Promise<R>
declare function wrapPromise<A1, A2, A3, R>(f: (a1: A1, a2: A2, a3: A3) => R): (a1: A1, a2: A2, a3: A3) => Promise<R>
declare function wrapPromise<A1, A2, A3, A4, R>(f: (a1: A1, a2: A2, a3: A3, a4: A4) => R): (a1: A1, a2: A2, a3: A3, a4: A4) => Promise<R>
// etc. 8 arguments should be enough for everyone :-P